Subgroups — #26225477

Order 12032.

1230 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251871	C₂	1	1	yes	maximal, characteristic, complemented
2	#20251852	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243926	C₂	1	2	yes	maximal, complemented
4	#20243911	C₂	1	2	yes	maximal, complemented
5	#20243782	C₂	1	2	yes	maximal, complemented
6	#20243772	C₂	1	2	yes	maximal, complemented
7	#20243492	C₂	1	2	yes	maximal, complemented
8	#20243363	C₂	1	2	yes	maximal, complemented
9	C₄₇×#3499	C₂	1	1	yes	maximal, characteristic
10	#15689890	C₂²	1	2	yes	—
11	#15689601	C₂²	1	2	yes	—
12	#15689140	C₂²	1	4	yes	—
13	#15689132	C₂²	1	4	yes	—
14	#15689107	—	2	2	no	—
15	#15689107	C₂²	1	2	yes	—
16	C₂×#13093943	—	2	2	no	—
17	C₂×#13093943	C₂²	1	2	yes	—
18	#15689097	—	2	4	no	—
19	#15689097	C₂²	1	2	yes	—
20	#15689097	C₂²	1	2	yes	—
21	#15688883	C₂²	1	4	yes	—
22	#15688879	C₂²	1	4	yes	—
23	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
25	D₄×Q₈×C₄₇	—	2	2	no	—
26	C₄₇×#547	—	2	2	no	—
27	C₄₇×#547	—	2	4	no	—
28	C₄₇×#536	C₄	1	2	yes	complemented
29	C₄₇×#536	C₄	1	2	yes	complemented
30	C₄₇×#536	C₂²	1	1	yes	characteristic
31	C₄₇×#536	C₂²	1	1	yes	characteristic
32	C₄₇×#532	C₄	1	2	yes	complemented
33	C₄₇×#532	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊Q₈×C₄₇	C₄	1	2	yes	complemented
35	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
37	#13094031	—	4	4	no	—
38	C₂×#10625329	—	2	4	no	—
39	C₂×#10625329	C₂³	1	4	yes	—
40	Q₈×Dic₄₇	—	4	4	no	—
41	#13093983	—	2	4	no	—
42	#13093983	C₂³	1	4	yes	—
43	#13093951	—	4	4	no	—
44	#13093948	—	4	4	no	—
45	#13093943	—	2	2	no	—
46	#13093943	—	2	4	no	—
47	#13093941	—	2	2	no	—
48	#13093939	—	2	4	no	—
49	#13093939	—	2	4	no	—
50	2₋¹⁺⁴×C₄₇	—	4	4	no	—
51	2₋¹⁺⁴×C₄₇	—	4	4	no	—
52	C₂×#41×C₄₇	—	2	1	no	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×#41×C₄₇	D₄	1	2	yes	—
57	C₂×#41×C₄₇	D₄	1	4	yes	—
58	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
59	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
60	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₄₇	—	2	1	no	—
62	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
63	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
64	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
65	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₄₇	—	2	4	no	—
68	C₄⋊Q₈×C₄₇	—	2	2	no	—
69	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
71	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
72	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
73	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
74	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
75	#124×C₄₇	C₂×C₄	1	2	yes	—
76	#124×C₄₇	C₂×C₄	1	2	yes	—
77	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
78	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
79	#123×C₄₇	—	2	4	no	—
80	#123×C₄₇	—	2	2	no	—
81	#123×C₄₇	—	2	4	no	—
82	#123×C₄₇	—	2	2	no	—
83	C₂²⋊Q₈×C₄₇	—	2	4	no	—
84	C₂²⋊Q₈×C₄₇	—	2	2	no	—
85	C₂²⋊Q₈×C₄₇	—	2	4	no	—
86	C₂²⋊Q₈×C₄₇	—	2	2	no	—
87	#121×C₄₇	—	2	4	no	—
88	#121×C₄₇	—	2	2	no	—
89	C₄×Q₈×C₄₇	—	2	1	no	—
90	C₄×D₄×C₄₇	—	2	2	no	—
91	C₄×D₄×C₄₇	—	2	1	no	—
92	C₄×D₄×C₄₇	—	2	4	no	—
93	C₄×D₄×C₄₇	—	2	2	no	—
94	#117×C₄₇	C₂×C₄	1	2	yes	—
95	#117×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	#41×C₄₇	—	2	4	no	—
101	#41×C₄₇	—	2	4	no	—
102	#41×C₄₇	—	2	4	no	—
103	#41×C₄₇	—	4	8	no	—
104	#41×C₄₇	—	4	4	no	—
105	#41×C₄₇	—	4	4	no	—
106	#41×C₄₇	—	4	4	no	—
107	#41×C₄₇	—	4	8	no	—
108	#41×C₄₇	—	4	4	no	—
109	C₂×Q₈×C₄₇	—	2	2	no	—
110	C₂×Q₈×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	4	no	—
112	C₂×Q₈×C₄₇	—	2	4	no	—
113	C₂×Q₈×C₄₇	—	4	4	no	—
114	C₂×Q₈×C₄₇	—	4	4	no	—
115	C₂×Q₈×C₄₇	—	4	4	no	—
116	C₂×Q₈×C₄₇	—	4	4	no	—
117	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
118	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₄₇	—	2	2	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
128	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
140	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₄⋊C₄×C₄₇	—	2	4	no	—
146	C₄⋊C₄×C₄₇	—	2	2	no	—
147	C₄⋊C₄×C₄₇	—	2	4	no	—
148	C₄⋊C₄×C₄₇	—	2	4	no	—
149	C₄⋊C₄×C₄₇	—	2	4	no	—
150	C₄⋊C₄×C₄₇	—	2	2	no	—
151	C₄⋊C₄×C₄₇	—	2	1	no	—
152	C₂²⋊C₄×C₄₇	—	2	2	no	—
153	C₂²⋊C₄×C₄₇	—	2	4	no	—
154	C₂²⋊C₄×C₄₇	—	2	2	no	—
155	C₂²⋊C₄×C₄₇	—	2	1	no	—
156	C₂²⋊C₄×C₄₇	—	2	4	no	—
157	C₂²⋊C₄×C₄₇	—	2	2	no	—
158	C₄²×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	—	2	1	no	—
160	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
162	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²⋊Dic₄₇	—	2	4	no	—
164	C₄⋊Dic₄₇	—	2	4	no	—
165	C₄⋊Dic₄₇	—	4	4	no	—
166	C₄×Dic₄₇	—	2	4	no	—
167	C₄×Dic₄₇	—	4	4	no	—
168	#10625329	—	2	4	no	—
169	#10625329	—	2	4	no	—
170	#10625329	—	4	4	no	—
171	C₂×C₄₇⋊C₈	—	2	4	no	—
172	C₂×C₄₇⋊C₈	—	4	4	no	—
173	C₂³×C₄₇	—	2	1	no	—
174	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₄₇	—	2	4	no	—
178	Q₈×C₄₇	—	2	2	no	—
179	Q₈×C₄₇	—	2	4	no	—
180	Q₈×C₄₇	—	2	2	no	—
181	Q₈×C₄₇	—	2	4	no	—
182	Q₈×C₄₇	—	2	2	no	—
183	Q₈×C₄₇	—	4	4	no	—
184	Q₈×C₄₇	—	4	4	no	—
185	Q₈×C₄₇	—	4	2	no	—
186	D₄×C₄₇	—	2	4	no	—
187	D₄×C₄₇	—	2	4	no	—
188	D₄×C₄₇	—	2	2	no	—
189	D₄×C₄₇	—	2	2	no	—
190	D₄×C₄₇	—	2	2	no	—
191	D₄×C₄₇	—	4	4	no	—
192	D₄×C₄₇	—	4	4	no	—
193	D₄×C₄₇	—	4	4	no	—
194	D₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	4	no	—
197	C₂×C₄×C₄₇	—	2	4	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	1	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	4	4	no	—
204	C₂×C₄×C₄₇	—	4	4	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	4	no	—
207	C₂×C₄×C₄₇	—	4	4	no	—
208	C₂×C₄×C₄₇	—	4	4	no	—
209	C₂×C₄×C₄₇	—	4	2	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
213	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
217	C₂×Dic₄₇	—	4	4	no	—
218	C₄₇⋊C₈	—	4	4	no	—
219	#21783	—	47	1	no	maximal, Sylow
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	4	1	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	—	4	2	no	—
225	C₂²×C₄₇	—	4	2	no	—
226	C₂²×C₄₇	—	4	1	no	—
227	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₄₇	#534	1	2	yes	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	4	no	—
233	C₄×C₄₇	—	4	2	no	—
234	C₄×C₄₇	—	4	1	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	4	1	no	—
237	C₄×C₄₇	#518	1	2	yes	—
238	C₄×C₄₇	#534	1	2	yes	—
239	Dic₄₇	—	8	4	no	—
240	#3499	D₄₇	1	1	yes	characteristic
241	#2889	—	47	1	no	—
242	#2884	—	47	1	no	—
243	#1912	—	47	2	no	—
244	#1909	—	47	2	no	—
245	#1886	—	47	2	no	—
246	#1884	—	47	2	no	—
247	#1827	—	47	2	no	—
248	#1796	—	47	2	no	—
249	C₂×C₄₇	—	2	2	no	—
250	C₂×C₄₇	—	2	1	no	—
251	C₂×C₄₇	—	4	2	no	—
252	C₂×C₄₇	—	4	2	no	—
253	C₂×C₄₇	—	8	1	no	—
254	C₂×C₄₇	#2308	1	1	yes	characteristic
255	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic
256	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic
257	#568	—	47	2	no	—
258	D₄×Q₈	—	2	2	no	—
259	#547	—	2	2	no	—
260	#547	—	2	4	no	—
261	#536	Dic₄₇	1	2	yes	complemented
262	#536	Dic₄₇	1	2	yes	complemented
263	#536	C₂×D₄₇	1	1	yes	characteristic
264	#536	C₂×D₄₇	1	1	yes	characteristic
265	#532	Dic₄₇	1	2	yes	complemented
266	#532	C₂×D₄₇	1	1	yes	characteristic
267	C₂×C₄⋊Q₈	Dic₄₇	1	2	yes	complemented
268	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
269	#519	—	47	2	no	—
270	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
271	#421	—	47	4	no	—
272	#419	—	47	4	no	—
273	#413	—	47	2	no	—
274	#413	—	94	2	no	—
275	C₂×#101	—	47	2	no	—
276	C₂×#101	—	94	2	no	—
277	#410	—	47	2	no	—
278	#410	—	47	2	no	—
279	#410	—	94	4	no	—
280	#339	—	47	4	no	—
281	H(3,ℤ/4)	—	47	4	no	—
282	C₄₇	#21783	1	1	yes	characteristic, complemented, Sylow
283	2₋¹⁺⁴	—	4	4	no	—
284	2₋¹⁺⁴	—	4	4	no	—
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	C₂×Dic₄₇	1	2	yes	—
288	C₂×#41	C₂×Dic₄₇	1	2	yes	—
289	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
290	C₂×#41	C₂²⋊D₄₇	1	4	yes	—
291	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
292	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
293	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
296	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
297	C₂²×Q₈	C₂²⋊D₄₇	1	2	yes	—
298	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
299	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
300	#131	—	188	4	no	—
301	C₂×M₁₆	—	47	4	no	—
302	C₂×M₁₆	—	94	4	no	—
303	C₄⋊Q₈	—	2	4	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
306	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
307	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
308	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
309	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
310	#127	C₂×Dic₄₇	1	1	yes	characteristic
311	#124	C₂×Dic₄₇	1	2	yes	—
312	#124	C₂×Dic₄₇	1	2	yes	—
313	#124	C₂×Dic₄₇	1	1	yes	characteristic
314	#124	C₂×Dic₄₇	1	1	yes	characteristic
315	#123	—	2	4	no	—
316	#123	—	2	2	no	—
317	#123	—	2	4	no	—
318	#123	—	2	2	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	#121	—	2	4	no	—
324	#121	—	2	2	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×Q₈	—	188	4	no	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	2	2	no	—
331	#117	—	47	4	no	—
332	#117	—	94	4	no	—
333	#117	C₂×Dic₄₇	1	2	yes	—
334	#117	C₂²×D₄₇	1	1	yes	characteristic
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
338	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
339	#104	—	188	4	no	—
340	#103	—	188	4	no	—
341	#101	—	94	4	no	—
342	#101	—	94	2	no	—
343	#100	—	94	2	no	—
344	#99	—	94	4	no	—
345	#99	—	94	4	no	—
346	#41	—	2	4	no	—
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	4	8	no	—
350	#41	—	4	4	no	—
351	#41	—	4	4	no	—
352	#41	—	4	4	no	—
353	#41	—	4	8	no	—
354	#41	—	4	4	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	4	4	no	—
360	C₂×Q₈	—	4	4	no	—
361	C₂×Q₈	—	4	4	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
364	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
365	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
366	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
367	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
368	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
369	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
374	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
375	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
376	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
377	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
378	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
386	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
387	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
388	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
389	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
390	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
391	M₁₆	—	94	4	no	—
392	M₁₆	—	94	4	no	—
393	M₁₆	—	188	4	no	—
394	C₂×C₈	—	94	4	no	—
395	C₂×C₈	—	188	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	94	4	no	—
404	C₄⋊C₄	—	188	4	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	94	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	94	4	no	—
415	C₄²	—	188	4	no	—
416	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
417	C₄²	C₂²×Dic₄₇	1	2	yes	—
418	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
419	C₂³	—	2	1	no	—
420	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
421	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
422	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
423	Q₈	—	2	4	no	—
424	Q₈	—	2	2	no	—
425	Q₈	—	2	4	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	2	4	no	—
428	Q₈	—	2	2	no	—
429	Q₈	—	4	4	no	—
430	Q₈	—	4	4	no	—
431	Q₈	—	4	2	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	4	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	188	4	no	—
458	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
459	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
460	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
461	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
463	C₂×C₄	#13094069	1	4	yes	—
464	C₈	—	188	4	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	1	no	—
472	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
473	C₂²	#15689682	1	2	yes	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	4	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	376	4	no	—
483	C₄	#15689598	1	2	yes	—
484	C₄	#15689682	1	2	yes	—
485	C₂	—	2	1	no	—
486	C₂	—	2	2	no	—
487	C₂	—	4	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	8	1	no	—
490	C₂	#20245966	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20245966
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3499	C₂
socle	C₂×C₄₇	#2308
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3499	D₄₇
hypocenter	C₄₇	#21783
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3499

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20251871	C₂	semidirect
2. #20251852	C₂	semidirect
3. #20243926	C₂	semidirect
4. #20243911	C₂	semidirect
5. #20243782	C₂	semidirect
6. #20243772	C₂	semidirect
7. #20243492	C₂	semidirect
8. #20243363	C₂	semidirect
28. C₄₇×#536	C₄	semidirect
29. C₄₇×#536	C₄	semidirect
32. C₄₇×#532	C₄	semidirect
34. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
261. #536	Dic₄₇	semidirect
262. #536	Dic₄₇	semidirect
265. #532	Dic₄₇	semidirect
267. C₂×C₄⋊Q₈	Dic₄₇	semidirect
282. C₄₇	#21783	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20251871	2
#20251852	2
#20243926	2
#20243911	2
#20243782	2
#20243772	2
#20243492	2
#20243363	2
C₄₇×#3499	2
#21783	47